Crystal filter circuit



Jan. 12, 1943. A. T, STARR 2,308,397

CRYSTAL FILTER CIRCUIT Filed Nov. 15, 1940 2 Sheets-Sheet 1 Fig. 2

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ke,/cm kq /cm 2 INVENTOR Patented J an. 12, 1943 CRYSTAL FILTER CIRCUITArthur Tisso Starr, Cheimsford, England, assignor toltadlo Corporationof America, a corporation of Delaware Application November 13, 1940,Serial No. 365,477 In Great Britain December 13, 1939 2 Claims.

The present invention relates to electric filter circuits, particularlyto crystal filter circuits.

The use of three-electrode piezo-electric crystals, that is,piezo-electric crystals having two electrodes on one face separated by anarrow gap and one electrode on the other face, as coupling elementsbetween circuits is known. The present invention arises out of therealization that threeelectrode piezo-eiectric crystals have certainadvantages which render them particularly suitable as elements in theconstruction and organization of filter circuits. For instance, wherepiezo-electric crystals, as ordinarily used, are employed in theconstruction of filter circuits, particularly of narrow pass-band filtercircuits, the designs are complicated by the necessity of neutralizingthe electrostatic capacitance of the crystal, but it is realized thatthe use of three electrode crystals,

in accordance with the present invention would result in an automaticneutralization of this capacitance.

According to the invention in its broadest aspe t a filter circuitincludes a three-electrode piezo-eiectric crystal having on one side twoelectrodes of equal or unequal area separated by a separating gap andtogether with the separating gap, covering the whole or part of saidconnected between the two electrodes on said one side of the crystal.

According to a feature of the present invention, a filter circuitincludes an input terminal, an output terminal, a second outputterminal, a three-electrode piezo-electrie crystal, having on one sidetwo electrodes of equal or unequal area separated by a separating gapand together with the separating gap, covering the whole or part of saidone side and on the other side a single electrode covering the whole orpart of said other side, a first connection between the fir inputterminal and one of said electrodes on said one side oi said crystal, asecond connection between the first said output terminal and the otherof said electrodes on said one side of said crystal, a direct connectionbetween said second I and output circuits.

a connection between the electrode on the said other side of saidcrystal and said direct connection, an impedance connecting said firstandsaid second connections, and impedances in the input pedances may beconnected one in the first said connection and the other in the secondsaid connection so that the three said impedances are in series, or theymay be connected one between the first said connection and said directconnection and the other between the second said connection and saiddirect connection. The impedances may be of any suitable form, forexample, crystals, inductances, or capacitances, or networks includingsuch elements. Preferably,though not necessarily, the electrodes of thethree-electrode piezo-electric crystal may be formed by plating thesurfaces of the crystal, and the areas of the two electrodes on one sidemay have any desired ratio according to the design of filter of whichthe crystal constitutes an element. Moreover the two electrodes on oneside, together with the separating gap may cover the whole of one sideand the third electrode on the other side may cover the whole of theother side, or the surfaces may be partially plated as described inBritish Patent 538,946/1941. Although usually, with a proper design ofcrystal holder direct capacitance between the two electrodes on one sideof the I nection with the accompanying drawings where- D in Figures 1 to7 inclusive, 9 and 10 represent dit said input terminal and said secondoutput terminal,

crystal is very small and thus renders such unnecessary, an earthedscreening electrode may.

if desired, be placed'between the two electrodes on said one side of thecrystal still furtherto reduce any direct capacitance between these twoelectrodes.

The invention will be further described in conagrammatically difierentfeatures of the invention in schematic circuit form, while Fig. '8 showsin cross-section a piezo-electric crystal the mode of vibration in whichis diagrammatically represented.

Referring first to Figs. '7 and 8, suppose the lower electrode to be atearth potential and the left and right hand upper electrodes to havepotentials er and en the piezo-electric effect manifests itself 'as aforce of Ice; per cm. and Ice: per cm. on-the edges of the halves of thecrystal.

Applying St. Venant principle of the elastic equivalence of staticallyequipollent systems of loads it will be found, even though the crystalis .by no means a long narrow bar, for which the principle holds'veryclosely, that theerror is not appreciable even for wide crystals, al-

The last mentioned imthough there must be some error. The application ofthe principle states that the crystal plate moves as though an averageforce of yzlc (Bi-H32) acts on the edges. There is then a chargeliberated per square centimeter of the electrode surface which is pportional to /2 (81-1-82). The constant of proportionality is found byconsidering the case of a fully plated crystal, for which totalcurrent=voltage-:-Q, where Q is either the impedance of a line or theseries resonant circuit .of the usual approximation. This means that iiand i: must be equal and such that their sum is given by This holds evenwhen one plate is opencircuited, for in such a case the current willfiow through the electrostatic capacitance, represented dotted in Fig. 7at C/I, across the plate concerned.

The equations of the three-electrode crystal may thus be written asi1=i2 (1) e1+ez=4Qii (2) The network can be drawn in pictorial form byrewriting the equations as 62: (81-4Qi1) or The latter form is chosenbecause of the symmetry. It is then clear that the complete system,including the electrostatic capacitance, may be represented by theequivalent networks of gs. i and 9. These figures relate to the casewhich the upper electrodes have equal areas. "2 the upper electrodeshave areas having the ratio :2 1 the equations become Fl in EEG in shuntwith a load Z1, and if a second valve has a grid load Z2, and if theelectrostatic capacitance V20 are assumed to be included respectively inZ1 and Z1, then q 3 I I I Q+ 1+Z The effect is thus of having a tunedcircuit coupling of inductance 4L, and decrement due to the crystal. Theband width may be varied by mistuning the side circuits.

1! an admittance Y be connected across the upper electrodes,

solving for e:

when Y is zero this expression reduces to that given above, but when Yis not zero there is seen to be considerable difference.

At frequencies well off-tune, Q is very large and then YY,+Y,Y,+Y,Y

If Y is at all comparable with Y1 and Y2 (Y1 and Y: being theadmittances of Z1 and Z3) the response becomes like that of anunneutraliud crystal circuit, with a finite response away from theresonant frequency, and a dip and rise near the resonant frequency.

Filters in accordance with the invention may take the forms shown inFigs. 3a and 4 wherein an impedance Z is placed between the upperelectrodes, and impedance Z1 are included in the input and outputconnections. Figs. 3b and 3c are the equivalent networks of Fig. 3a. Thedifference between Fig. 3a and Fig. 4 is the positioning of Z1 Z1.

It will be noted that with Z= and 21:0 Fig. 3c becomes 3d or 3e so thatthe latter hold for general and not only for restricted equivalence.Fig. 3e is the lattice equivalent of the neutralized crystal (seeElectric Circuits and Wave Filters," A. T. Starr, 2nd edition, Figures174 and 335. Z1 could, as in Fig. 4, be in parallel at the input andoutput and then the equivalent lattice has Z1 as a shunt arm in its fourbranches.

Since Fig. 3c represents a general lattice, an unbalanced equivalent ofany balanced circuit arrangement can be obtained by the use of a circuitemploying a three-electrode crystal.

As stated, the irnpedances (Z and Z1) may take various forms. Thus, if Zis a crystal and Z1 an inductance, the network becomes the unbalancedform of the balanced lattice broad-band filter so often used in highgrade crystal filters for carrier telephony and single side bandworking. Z1 may be a series or shunt arm. Among the advantages to bederived from this filter may be mentioned that a filter with animpedance approximately one-quarter of the lattice form can beconstructed. Thus for a filter with an unsymmetrical attenuationcharacteristiaone crystal has a low impedance and, the other a high, andthe impedance is then limited by the low impedance crystal. It is seenfrom Fig. 3c that the equivalent lattice must have crystals of impedanceQ and %Z, while the three-electrode crystal system has crystals ofimpedance Q and Z. If, therefore, the Z arm be chosen as the lowimpedance crystal, the impedance of the filter can be one fourth of thevalue in the lattice form. Moreover the high impedance crystal will haverather more plating than that in the lattice form (in which its platingis rather scanty) and it will have only one pair of electrodes.

In the case of a filter in which Zi=0 and Z is a series-tuned circuit(Llcl) with parallel capacitance (C2) thecrystal arm has a moat I: and apole at l=h(1+%r). If L101 resonates at I: a broad pass band from fr toIs is produced. where his the resonant frequency of the crystal Theimpedances oi the arms are shown in Fig. 5. The upper cut-oi! can bevaried by varying Cs. Such a filter is easy to construct and to adjust.

. an output terminal and a return lead common to the input and outputcircuits thereoi, a first impedance connected between said input andoutput terminals, a second impedance connected between the inputterminal and said return lead, a third impedance connected between saidoutput terminal and said return lead, and a piezoelectric device havingon one side two electrodes connected respectively to the input andoutput terminals, and on the other side a single electrode connected tosaid common return lead, said two electrodes on the one side of saidpiezo-ele ctric l0 device being of different areas the ratio betweenwhich is adjusted to provide a. balance between the input and outputimpedances vof said filter network.

2. A filter network according to claim 1 in 15 which the firstsaidimpedance is inductive,

ARTHUR TISSO STARR.

